Historical Perspectives on Math and Science Timeline-John Bard

Paradoxes of Division-Brahmagupta

628

Indian mathematician stated that 0/0 is 0.

Paradoxes of Division- Bhaskara

1150

Argued that a quantity divided by zero yields an infinite quantity.

Age of the Earth- Bishop James Ussher

1650

The Anglican Bishop published a 1600 page work titled "The Annals of the World" where he used detailed readings of the Bible and other sources to determine the date of the creation of the world to be October 23, 4004 B.C.

Infinitely Small-Newton and Leibniz

1670

Both calculated instantaneous speed using infinitesimals, but they did not regard them as numbers due to the logical inconsistency that resulted from the use of them as numbers. Leibniz himself called them "useful fictions."
The following extended response gives more insight into the views of both Newton and Leibniz as well as a link to a great video explaining the mathematics of infinitesimals: https://docs.google.com/document/d/1QUiIsRiqLQGbFWB7F4BMcwox_qSLBhvaDIQdIeHLGhc/edit

Infinitely Small-Marquis L'Hospital

1696

Wrote first calculus textbook stating that two values differing by an infinitesimal can be treated as equal. He thought infinitesimals were at the same time both equal and unequal to 0 and exist as numbers.

Infinitely Small- George Berkeley

1734

Gave strong criticism against infinitesimals and the reality of instantaneous speed at all. Instantaneous velocity was a physical impossibility.

Age of the Earth-Benoit de Maillet

1738

Estimated the Age of the Earth to be 2 billion years old.

Age of the Earth-Georges Buffon

1749

Used measurements on a ball of cooling iron to estimate the earth as 70 thousand years old.

Paradoxes of Division- Leonhard Euler

1770

The Swiss mathematician gave the result that a quantity divided by 0 gives infinity in his textbook "Complete Introduction to Algebra."

Paradoxes of Division- Martin Ohm

1828

Argued that division by 0 is meaningless, and he advised his readers to "Never divide by 0."

Age of the Earth-Lord Kelvin

1862

Modeled the earth as a cooling molten core and used his knowledge of thermodynamics to calculate the age of the earth to be between 20-400 million years old. His formal estimate was 98 million years.
More discussion of Lord Kelvin's involvement in the Age of the Earth debate is available at the following link: https://docs.google.com/document/d/1Jch6FZti6NPhaWBOgEL5kwYN35e27ln-psVzq5E8VHs/edit

Discovery of the Electron- William Crookes

1869

Invented the Crookes Tube, which would be the device necessary for many of the early experiments in the discovery of the electron. It is of note that the Crookes Tube was later known as the Cathode Ray Tube.

Infinitely Small-Karl Weierstrass

1870

Though the infinitesimal ds/dt that has long been used to calculate instantaneous velocity is just an archaic way of expressing a limit. Believed infinitesimals not reality, they were just a crude representation of limits.

Discovery of the Electron-Arthur Schuster

1884

Calculated charge to mass ratio bounds for the yet to be identified electron.

Discovery of the Electron-J.J. Thomson

1897

Proposed negatively-charged electron as a fundamental particle after cathode ray tube experiments. Credited as discoverer of the electron.
More discussion of cathode rays and the experiments of J.J. Thomson is available with a great video explanation of one of his experiments at the following link: https://docs.google.com/document/d/1otsEXeR6DLdcTea2-IHXIgmJ3AyIgDs9HripmXbmyOw/edit

Discovery of the Electron- Jean-Baptiste Perrin

1897

Theorized that the cathode ray was composed of negatively charged particles that were from residual gas in tube being split apart.

DIscovery of the Electron-Robert Millikan

1909

Accurately determined the charge of an electron.

Age of the Earth-George Arthur Holmes

1927

Used radiometric dating to calculate the age of the earth to be between 1.6 and 3 billion years. Published this in "The Age of the Earth, an Introduction to Geological Ideas."

Infinitely Small-Abraham Robinson

1960

Devised new and more encompassing numerical system known as nonstandard analysis. Believed that infinitesimals were formal objects that behaved as numbers and were coined "nonstandard numbers."

Paradoxes of Division- James Anderson

2006

Pioneered a form of arithmetic known as transreal arithmetic. In this system of numbers a quantity divided by 0 is infinity, a negative number divided by zero is a negative quantity, and 0 divided by 0 a number known as nullity.
For a more robust discussion of transreal arithmetic and James Anderson's contributions to the topic, please refer to the extended response at the following link: https://docs.google.com/document/d/1RQai1Q2W9gTZVOUpWGBX7TnvE1bsOc4JfJSvsvpFOW0/edit